Velocity-matching model for electron capture in keV atomic collisions

We develop an approximate integral for the amplitudes of electron transfer in ion-atom collisions. The resulting model pertains to collisions involving low-n excited states and relative ion-atom velocities near the average speed of the target valence electron. Three points are essential to the derivation: (1) the atomic states are treated as a dielectric taking into account the long-range interaction, (2) the process is viewed in momentum space quantifying the idea of velocity matching, and (3) a semianalytic expression is derived using the Born approximation. From the resulting integral propensity rules are derived telling which final states are favored based on the initial target state and parameters of the collision. {} 1996 The American Physical Society.